The purpose of the work is to study the influence of the control of the elastic and damping characteristics of the cushioning system based on the use of magnetorheological elastomers on the smoothness of the course of wheeled transport vehicles. The technique. The research used the methods of: magnetic field theory, the theory of vehicle suspension, experiment theory planning, and the FEMM code for studying magnetic field characteristics and mathematical modeling of wheeled vehicle movement along roughness in the Delphi environment. Results. Designed, researched and patented designs of elastic hinges of the suspension arms with magnetorheological elastomers. The relative boundaries of changes in the elastic modules and losses of these hinges are determined when controlling the characteristics of the suspension in order to improve the smoothness of the wheeled vehicle. Scientific novelty. For the first time, the feasibility of using magnetorheological elastomers to control the elastic and damping characteristics of the cushioning system of wheeled vehicles has been investigated, and the requirements for control laws have been determined, which make it possible to increase smoothness by more than 40 %; it is established that the control of the loss modulus has a greater effect on the improvement of smoothness of motion than the control of the elastic modulus. Practical value. The design has been developed and the relative boundaries of changes in the modules of elasticity and loss of hinges with magnetorheological elastomers during their control have been determined, which will make it possible to formulate requirements for elastomers when developing promising hinge designs for vehicle suspension systems. References 21, figures 18.